1. What is the total number of outcomes for a player to draw a “Royal Flush” fro

Question

1. What is the total number of outcomes for a player to draw a “Royal Flush” from a deck of poker cards? What is the probability for a player to draw a “Royal Flush” in a five-card stud game?

2. What is the total number of outcomes for a player to draw a “Straight Flush” from a deck of poker cards? What is the probability for a player to draw a “Straight Flush” in a five-card stud game?

3.What is the total number of outcomes for a player to draw a “Four of a kind” from a deck of poker cards? What is the probability for a player to draw a “Four of a kind” in a five-card stud game?

Explanation / Answer

Solution:-

1. A ROYAL FLUSH

This consists of the ten, jack, queen, king, and ace of one suit. There are four such hands. The probability is 0.00000153908.

2. A STRAIGHT FLUSH

All 5 cards are from the same suit and they form a straight (they may also be a royal flush). The number of such hands is 4*10, and the probability is 0.0000153908.

IF YOU MEAN TO EXCLUDE ROYAL FLUSHES, SUBTRACT 4 (SEE THE NEXT TYPE OF HAND): the number of hands would then be 4*10-4 = 36, with probability approximately 0.0000138517.

3. FOUR OF A KIND

This hand has the pattern AAAAB where A and B are from distinct kinds.

The number of such hands is (13-choose-1)(4-choose-4)(12-choose-1)(4-choose-1).

The probability is 0.000240

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